Attractor for Lattice System of Dissipative Zakharov Equation  

作　　者：Fu Qi YIN Sheng Fan ZHOU Zi Gen OUYANG Cui Hui XIAO 

机构地区：[1]School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, P. R. China [2]Mathematics and Science College of Shanghai Normal University, Shanghai 200234, P. R. China [3]School of Mathematics and Physics of University of South China, Hengyang 421001, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2009年第2期321-342,共22页数学学报（英文版）

基　　金：supported by National Natural Science Foundation of People's Republic of China (10771139);Partly supported by A Project Supported by Scientific Research Fund of Hu'nan Provincial Education on Department (08A070; 08A071)

摘　　要：We consider the asymptotic behavior of solutions of an infinite lattice dynamical system of dissipative Zakharov equation. By introducing new weight inner product and norm in the space and establishing uniform estimate on ＂Tail End＂ of solutions, we overcome some difficulties caused by the lack of Sobolev compact embedding under infinite lattice system, and prove the existence of the global attractor; then by using element decomposition and the covering property of a polyhedron in the finite-dimensional space, we obtain an upper bound for the Kolmogorov ε-entropy of the global attractor; finally, we present the upper semicontinuity of the global attractor.We consider the asymptotic behavior of solutions of an infinite lattice dynamical system of dissipative Zakharov equation. By introducing new weight inner product and norm in the space and establishing uniform estimate on ＂Tail End＂ of solutions, we overcome some difficulties caused by the lack of Sobolev compact embedding under infinite lattice system, and prove the existence of the global attractor; then by using element decomposition and the covering property of a polyhedron in the finite-dimensional space, we obtain an upper bound for the Kolmogorov ε-entropy of the global attractor; finally, we present the upper semicontinuity of the global attractor.

关 键 词：Zakharov Equation global attractor infinite lattice system Kolmogorov ε-entropy uppersemicontinuity 

分 类 号：O174[理学—数学]